I got it, I think. You need to play
around with the -width()- option in
-xtdes-. I surmise that the default
is not big enough for your data.

My first thought was: "What width option? There is no "width" option
listed for -xtdes- in the [XT] manual." But I see it is listed in the
on-line help -- and sure enough, in my panel of i=50 and t=140, if I
either drop enough observations so that t=100 or I add ", width(200)"
to the -xtdes- command, I now -- correctly -- am told

(i*t uniquely identifies each observation)

whereas before I was told otherwise. Good catch, Nick!

Which brings me to the question: why even bother setting a default
width, let alone setting it so low? This arguably isn't very intuitive
(look at the time wasted by the OP), and with "wide" panels of data
becoming ever more common as time goes on (pun intended), perhaps this
limit could be raised (or dropped altogether) the next time an update
to the ado files is made?